Examining what seems at first to be purely aspectual morphemes in wolof, this paper will first bring to light the puzzling polysemy of these. On the face of it, the variation in meaning appears to be quite similar in the different aspectual morphemes and can be expressed by the following rule : aspectual specifications yield a temporal expression with dynamic verbs (which is well known) and turn into modal specifications with stative verbs. This shift from time to modality can be quite easily explained within the framework of the theory of enunciation. As a matter of fact, within this theory, the meaning of an utterance results from the relationship with the situation in which the speaker is speaking. The so-called "situation of utterance" is defined by to variables (1) the speaker or "subject of enunciation", who endorses the utterance and who is therefore the source of the modal specifications, (2) the time of utterance, which is the origin of the temporal and spatial specifications.Through this system, we can both explain the polysemy displayed in the aspectual markers and argue that the subject of enunciation does not only stand for the part of the subjectivity involved in language but must be considered as the ultimate source of specifications in the construction of meaning.